Issue connecting animation to character in Blender Game Engine
The documentation says:


  The Action actuator is only visible when an armature is selected,
  because actions are stored in the armature.


But this seems to be no longer true you can add the Action actuator to all objects this might cause the problem.

Try a setup like that (On your armature) with your start and end frame 1..25, Loop Stop (which actually means Loop Start -Play ipo continuously from start to end when a TRUE pulse is received.)